*2.1. Problem Definition*

The steady flow of a non-Newtonian fluid containing gold nanoparticles over a porous curved surface was examined. According to Chen [31], blood is treated as an electric conducting fluid. Thus, blood flow in nature is magnetohydrodynamic. Blood flow is due to the movement of the stretching surface along the *s* direction and suction along the *r* direction. In addition, the stretching curve is coiled in a circle of radius *R* and center *O* and contains 12–85 nm gold nanoparticles, as shown in Figure 1. A magnetic field *B*0 is applied normal to the curved surface. A larger *R* signifies a vaguely curved surface. Moreover, the stretching and shrinking sheet of the curved surface depends upon the arbitrary constant (*c* > 0 for stretching and *c* < 0 for shrinking), where velocity is represented as *Uw*(*s*) = *cs*, with *c* > 0, which moves along the *s* direction, and suction velocity is represented as *vo*. In addition, the characteristics of nanoparticles and the carrier-based fluid are assumed to be constant. The temperature and ambient temperature of the surface are represented, respectively, as *Tw* and *T*<sup>∞</sup>. The radiation and partial slip effects are also incorporated.

**Figure 1.** Physical diagram of the problem.
